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Temporal and modal logic
 HANDBOOK OF THEORETICAL COMPUTER SCIENCE
, 1995
"... We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic. ..."
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Cited by 1107 (16 self)
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We give a comprehensive and unifying survey of the theoretical aspects of Temporal and modal logic.
A Propositional Modal Logic of Time Intervals
 Journal of the ACM
, 1996
"... : In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a gener ..."
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Cited by 119 (2 self)
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: In certain areas of artificial intelligence there is need to represent continuous change and to make statements that are interpreted with respect to time intervals rather than time points. To this end we develop a modal temporal logic based on time intervals, a logic which can be viewed as a generalization of pointbased modal temporal logic. We discuss related logics, give an intuitive presentation of the new logic, and define its formal syntax and semantics. We make no assumption about the underlying nature of time, allowing it to be discrete (such as the natural numbers) or continuous (such as the rationals or the reals), linear or branching, complete (such as the reals) or not (such as the rationals). We show, however, that there are formulas in the logic that allow us to distinguish all these situations. We also give a translation of our logic into firstorder logic, which allows us to apply some results on firstorder logic to our modal one. Finally, we consider the difficulty o...
METATEM: A Framework for Programming in Temporal Logic
 In REX Workshop on Stepwise Refinement of Distributed Systems: Models, Formalisms, Correctness (LNCS Volume 430
, 1989
"... In this paper we further develop the methodology of temporal logic as an executable imperative language, presented by Moszkowski [Mos86] and Gabbay [Gab87, Gab89] and present a concrete framework, called METATEM for executing (modal and) temporal logics. Our approach is illustrated by the developmen ..."
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Cited by 88 (20 self)
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In this paper we further develop the methodology of temporal logic as an executable imperative language, presented by Moszkowski [Mos86] and Gabbay [Gab87, Gab89] and present a concrete framework, called METATEM for executing (modal and) temporal logics. Our approach is illustrated by the development of an execution mechanism for a propositional temporal logic and for a restricted first order temporal logic.
Automated Temporal Reasoning about Reactive Systems
, 1996
"... . There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective a ..."
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Cited by 39 (2 self)
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. There is a growing need for reliable methods of designing correct reactive systems such as computer operating systems and air traffic control systems. It is widely agreed that certain formalisms such as temporal logic, when coupled with automated reasoning support, provide the most effective and reliable means of specifying and ensuring correct behavior of such systems. This paper discusses known complexity and expressiveness results for a number of such logics in common use and describes key technical tools for obtaining essentially optimal mechanical reasoning algorithms. However, the emphasis is on underlying intuitions and broad themes rather than technical intricacies. 1 Introduction There is a growing need for reliable methods of designing correct reactive systems. These systems are characterized by ongoing, typically nonterminating and highly nondeterministic behavior. Examples include operating systems, network protocols, and air traffic control systems. There is w...
Reasoning about Time in the Situation Calculus.
, 1995
"... We extend the ontology of the situation calculus to provide for the representation of time and event occurrences. We do this by defining a time line corresponding to a sequence of situations (called actual situations) beginning with the initial situation. Actual situations are totally ordered and ..."
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Cited by 36 (4 self)
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We extend the ontology of the situation calculus to provide for the representation of time and event occurrences. We do this by defining a time line corresponding to a sequence of situations (called actual situations) beginning with the initial situation. Actual situations are totally ordered and the actions that lead to different actual situations are said to have occurred. This exension to the situation calculus permits one to express truths about the state of the world at different times. For example, we can state that at some point in the future certain fluent will be true. We can also express constraints on the occurrences of events, for example, that after releasing a cup, it will eventually hit the floor. Our version of the situation calculus subsumes other temporal logics. In particular, we show that the modal Temporal Logic of Concurrency [4] can be embedded in the extended situation calculus. Our extension can also realize the essential features of other first ord...
Hyperdocuments as Automata: Tracebased Browsing Property Verification
 In Proceedings of the 1992 European Conference on Hypertext (ECHT92: November 30December 4
, 1992
"... In many hypertext systems, meaningfully traversing a document depends on capabilities, features, and navigational aids that are part of the browser implementation. For example, if a reader browses to a node that has no out links, then backing up, or "warping" to the table of contents can allow the b ..."
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Cited by 27 (10 self)
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In many hypertext systems, meaningfully traversing a document depends on capabilities, features, and navigational aids that are part of the browser implementation. For example, if a reader browses to a node that has no out links, then backing up, or "warping" to the table of contents can allow the browsing session to continue. If hyperdocuments are to become interchangeable among hypertext systems, rather than being readable only on the systems from which they are authored, one obvious but complex approach is to try and standardize on (most likely, very many) browsing features and behaviors, forming some standard union of the capabilities of current major implementations. This approach molds (or perhaps restricts) future systems, since new browsing "features" must then be worked into such a standard. An alternate approach, used in this paper, is to deemphasized browser features and emphasize inherent document structure with browsing semantics. An author should be able to create docume...
Hyperdocuments as Automata: Verification of Tracebased Browsing Properties by Model Checking
, 1997
"... As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union" of ex ..."
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Cited by 26 (3 self)
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As hypertext systems proliferate and as networks become more ubiquitous, an important problem is to determine how to provide hyperdocument interoperability. Instead of taking the approach of standardizing, and implementing, a large and complex set of browsing features gleaned from some "union" of existing systems, we present an approach that allows each document to encode its own browsing semantics in the links of the hyperdocument. Any implementation offering the "follow link" operation can then simulate the intent of the author. The method requires a mental shift in how a hyperdocument is viewed abstractly. Instead of treating the links of a document as defining a static directed graph, they are thought of as defining an abstract program, termed the linksautomaton of the document. A branching temporal logic notation, termed HTL*, is introduced for specifying properties a document should exhibit during browsing. An automated program verification technique called model checking is ...
On the Decidability of Continuous Time Specification Formalisms
 Journal of Logic and Computation
, 1998
"... We consider an interpretation of monadic secondorder logic of order in the continuous time structure of finitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving tran ..."
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Cited by 9 (5 self)
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We consider an interpretation of monadic secondorder logic of order in the continuous time structure of finitely variable signals and show the decidability of monadic logic in this structure. The expressive power of monadic logic is illustrated by providing a straightforward meaning preserving translation into monadic logic of three typical continuous time specification formalism: Temporal Logic of Reals [2], Restricted Duration Calculus [4], and the Propositional fragment of Mean Value Calculus [6]. As a byproduct of the decidability of monadic logic we obtain that the above formalisms are decidable even when extended by quantifiers. 1 Introduction In the recent years systems whose behavior change in the continuous (real) time were extensively investigated. Hybrid and control systems are prominent examples of real time systems. A number of formalisms for specification of real time behavior were suggested in the literature. Some of these formalisms (e.g., timed automata [1]) exten...
Propositional interval neighborhood temporal logics
 Journal of Universal Computer Science
, 2003
"... Abstract: Logics for time intervals provide a natural framework for dealing with time in various areas of computer science and artificial intelligence, such as planning, natural language processing, temporal databases, and formal specification. In this paper we focus our attention on propositional i ..."
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Cited by 7 (4 self)
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Abstract: Logics for time intervals provide a natural framework for dealing with time in various areas of computer science and artificial intelligence, such as planning, natural language processing, temporal databases, and formal specification. In this paper we focus our attention on propositional interval temporal logics with temporal modalities for neighboring intervals over linear orders. We study the class of propositional neighborhood logics (PNL) over two natural semantics, respectively admitting and excluding pointintervals. First, we introduce interval neighborhood frames and we provide representation theorems for them; then, we develop complete axiomatic systems and semantic tableaux for logics in PNL.
Expressive Completeness of Duration Calculus
 Information and Computation
, 2000
"... This paper compares the expressive power of firstorder monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of the Propositional version of Duration Calculus (PDC), a formalism for the specification of realtime systems. Our results show that ..."
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Cited by 6 (1 self)
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This paper compares the expressive power of firstorder monadic logic of order, a fundamental formalism in mathematical logic and the theory of computation, with that of the Propositional version of Duration Calculus (PDC), a formalism for the specification of realtime systems. Our results show that the propositional duration calculus is expressively complete for firstorder monadic logic of order. Our semantics for PDC conservatively extends the standard one to all positive (including infinite) length intervals. Hence, in view of the expressive completeness, liveness properties can be specified in PDC. This observation refutes a widely believed misconception that the Duration Calculus cannot specify liveness properties. 1 Introduction The Duration Calculus (DC for brevity) [22] is a formalism for the specification of real time systems. The Duration Calculus is based on interval logic [9] and uses real numbers to model time. DC has been successfully applied in case studies of software...